Help troubleshooting SqlException: Timeout expired on connection, in a non-load situation

Question

I have a server hosting a website of mine that has almost zero-traffic.
A few people (< 20) enter the site every day, and a few RSS readers are subscribed to some fee

Answer 1

It smells a cronned thing that runs at the same time. As RBarryYoung says.. some nightly backup or it could be something else Do you have root access to the server? Can you see the crontabs?

Could it be some full text indexing plugin on top of the SQL server that runs its reindexing procedures close to the time you are experiencing the issues?